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Estimating transmission noise on networks from stationary local order (2405.12023v1)

Published 20 May 2024 in cond-mat.stat-mech and physics.soc-ph

Abstract: In this paper we study networks of nodes characterised by binary traits that change both endogenously and through nearest-neighbour interaction. Our analytical results show that those traits can be ranked according to the noisiness of their transmission using only measures of order in the stationary state. Crucially, this ranking is independent of network topology. As an example, we explain why, in line with a long-standing hypothesis, the relative stability of the structural traits of languages can be estimated from their geospatial distribution. We conjecture that similar inferences may be possible in a more general class of Markovian systems. Consequently, in many empirical domains where longitudinal information is not easily available the propensities of traits to change could be estimated from spatial data alone.

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References (53)
  1. Application of phylogenetic networks in evolutionary studies. Molecular Biology and Evolution, 23:254–267, 2005.
  2. Uri Alon. Network motifs: theory and experimental approaches. Nat Rev Genet., 8(, 2007.
  3. Language is a complex adaptive system: Position paper. Language Learning, 59(s1):1–26, 2009.
  4. Fixation and consensus times on a network: A unified approach. Phys. Rev. Lett., 101:258701, 2008.
  5. Statistical physics of social dynamics. Rev. Mod. Phys., 81:591–646, 2009.
  6. Mathematics of Epidemics on Networks From Exact to Approximate Models. Springer International Publishing, 2017.
  7. The study of structured populations—new hope for a difficult and divided science. Nat. Rev. Genet., 4:535–543, 2003.
  8. Inferring the parameters of a markov process from snapshots of the steady state. Journal of Statistical Mechanics: Theory and Experiment, 2018(2):023403, feb 2018.
  9. Estimate of the Mutation Rate per Nucleotide in Humans. Genetics, 156(1):297–304, 09 2000. doi: 10.1093/genetics/156.1.297.
  10. Patricia L. Foster. Methods for determining spontaneous mutation rates. In DNA Repair, Part B, volume 409 of Methods in Enzymology, pages 195–213. Academic Press, 2006.
  11. Determining mutation rates in bacterial populations. Methods, 20(1):4–17, 2000.
  12. Joseph H. Greenberg. Language typology: a historical and analytic overview. The Hague: Mouton, 1974.
  13. Geospatial distributions reflect temperatures of linguistic features. Science Advances, 7(1):eabe6540, 2021.
  14. The supplement contains further details of the model and the theoretical and numerical analysis (url to be inserted by copy editor), 2024.
  15. The noisy voter model. Stochastic Processes and their Applications, 55(1):23–43, 1995.
  16. The noisy voter model on complex networks. Scientific Reports, 6(1):1–14, 2016.
  17. Stochastic pair approximation treatment of the noisy voter model. New Journal of Physics, 20(10):103045, 2018.
  18. Analytical solution of the voter model on uncorrelated networks. New Journal of Physics, 10(6):063011, 2008.
  19. Sidney Redner. Reality-inspired voter models: A mini-review. Comptes Rendus Physique, 20(4):275–292, 2019. ISSN 1631-0705.
  20. Note1. The quantity τ𝜏\tauitalic_τ can take negative values. This describes systems with anti-correlations between neighbouring spins. For details see Sec. S8.2 in the SM.
  21. Heterogeneous pair approximation for voter models on networks. Europhys. Lett., 88:58004, 2009.
  22. Matthew S. Dryer and Martin Haspelmath, editors. WALS Online (v2020.3). Zenodo, 2013. doi: 10.5281/zenodo.7385533. URL https://doi.org/10.5281/zenodo.7385533.
  23. James P Gleeson. Binary-state dynamics on complex networks: Pair approximation and beyond. Physical Review X, 3(2):021004, 2013.
  24. Sergey Dorogovtsev. Lectures on Complex Networks. Oxford University Press, 02 2010.
  25. Mark EJ Newman. Assortative mixing in networks. Physical review letters, 89(20):208701, 2002.
  26. The configuration model for barabasi-albert networks. Applied Network Science, 4(1):1–13, 2019.
  27. Andreas Knoblauch. Closed-form expressions for the moments of the binomial probability distribution. SIAM Journal on Applied Mathematics, 69(1):197–204, 2008.
  28. Albert-László Barabási. Network science. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1987):20120375, 2013.
  29. Mark Newman. Networks. Oxford university press, 2018.
  30. Neil JA Sloane. The on-line encyclopedia of integer sequences. In Towards mechanized mathematical assistants, pages 130–130. Springer, 2007.
  31. Concrete mathematics: a foundation for computer science. Computers in Physics, 3(5):106–107, 1989.
  32. Analytic combinatorics. cambridge University press, 2009.
  33. Maxie D Schmidt. A short note on integral transformations and conversion formulas for sequence generating functions. Axioms, 8(2):62, 2019.
  34. Integrals and series: direct laplace transforms. Routledge, 2018.
  35. Giuseppe Lauricella. Sulle funzioni ipergeometriche a piu variabili. Rendiconti del Circolo Matematico di Palermo, 7(1):111–158, 1893.
  36. Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions. Cambridge University Press, 2020.
  37. Jordan Abbott. Laplace transforms of products of modified bessel functions, Mar 2022. URL https://math.stackexchange.com/questions/4404226/laplace-transforms-of-products-of-modified-bessel-functions.
  38. Pi and the AGM: a study in the analytic number theory and computational complexity. Wiley-Interscience, 1987.
  39. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 1988.
  40. JL Burchnall. Differential equations associated with hypergeometric functions. The Quarterly Journal of Mathematics, (1):90–106, 1942.
  41. More Special Functions (Integrals and Series vol 3). Gordon and Breach, New York, 1990.
  42. Hypergeometric functions and elliptic integrals. Current topics in analytic function theory, pages 48–85, 1992.
  43. Ian M Wanless. Counting matchings and tree-like walks in regular graphs. Combinatorics, Probability and Computing, 19(3):463–480, 2010.
  44. On the generating function of the catalan sequence: a historical perspective. Congressus Numerantium, pages 97–108, 2001.
  45. Richard P Stanley. Catalan numbers. Cambridge University Press, 2015.
  46. The geometry of ecological interactions: simplifying spatial complexity. Cambridge University Press, 2000.
  47. Christopher Kitching. Estimating transmission noise on networks from stationary local order, May 2024. URL https://github.com/C-Kitching/Estimating-transmission-noise-on-networks-from-stationary-local-order.
  48. Clayton W Commander. Maximum cut problem, max-cut. Encyclopedia of Optimization, 2, 2009.
  49. D. Dediu. Proc. R. Soc. B, 278:474–479, 2011.
  50. Sarah Boslaugh. Statistics in a nutshell: A desktop quick reference. ” O’Reilly Media, Inc.”, 2012.
  51. Roger W Johnson. An introduction to the bootstrap. Teaching statistics, 23(2):49–54, 2001.
  52. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. Journal of clinical epidemiology, 64(2):163–171, 2011.
  53. An atlas of functions. Taylor & Francis/Hemisphere, 1987.
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